# Describe A + B

• Oct 17th 2011, 08:44 AM
Lolyta
Describe A + B
Hello. I don't know how to do this(Doh)
A = {$\displaystyle (x_1,x_2): x_1=0, 0 \leq x_2 \leq 1$}
B = {$\displaystyle (x_1,x_2): x_2=2, 0 \leq x_1 \leq 1$}

Describe A+B and A-B.

Thank you.
• Oct 17th 2011, 08:55 AM
TheChaz
Re: Describe A + B
Well, these are line segments...

Do you know what "+" and "-" mean in this context?
• Oct 17th 2011, 08:57 AM
alexmahone
Re: Describe A + B
Quote:

Originally Posted by TheChaz
Well, these are line segments...

They look like coordinates to me.

Edit: I see what you mean. But + and - seem to me to be simple addition and subtraction of real coordinates.
• Oct 17th 2011, 09:12 AM
TheChaz
Re: Describe A + B
Quote:

Originally Posted by alexmahone
They look like coordinates to me.

Indeed, the elements of A and B are coordinates, but isn't the entire set A (B) a line segment/interval of R^2?

Since A and B aren't real numbers... ??? (Smirk)
• Oct 17th 2011, 09:15 AM
alexmahone
Re: Describe A + B
Quote:

Originally Posted by Lolyta
Hello. I don't know how to do this(Doh)
A = {$\displaystyle (x_1,x_2): x_1=0, 0 \leq x_2 \leq 1$}
B = {$\displaystyle (x_1,x_2): x_2=2, 0 \leq x_1 \leq 1$}

Describe A+B and A-B.

Thank you.

A + B = {$\displaystyle (x_1,x_2): 0 \leq x_1 \leq 1, 2 \leq x_2 \leq 3$}
A - B = {$\displaystyle (x_1,x_2): -1 \leq x_1 \leq 0, -2 \leq x_2 \leq -1$}
• Oct 17th 2011, 09:17 AM
alexmahone
Re: Describe A + B
Quote:

Originally Posted by TheChaz
Indeed, the elements of A and B are coordinates, but isn't the entire set A (B) a line segment/interval of R^2?

Since A and B aren't real numbers... ??? (Smirk)

Sorry...
• Oct 17th 2011, 12:15 PM
Lolyta
Re: Describe A + B
Quote:

Originally Posted by alexmahone
A + B = {$\displaystyle (x_1,x_2): 0 \leq x_1 \leq 1, 2 \leq x_2 \leq 3$}
A - B = {$\displaystyle (x_1,x_2): -1 \leq x_1 \leq 0, -2 \leq x_2 \leq -1$}

Thanks a lot for answering but could you explain how you did it?
• Oct 17th 2011, 12:24 PM
Plato
Re: Describe A + B
Quote:

Originally Posted by Lolyta
Thanks a lot for answering but could you explain how you did it?

We cannot help until you define what each of $\displaystyle A+B~\&~A-B$ means.
• Oct 18th 2011, 06:01 AM
Lolyta
Re: Describe A + B
Quote:

Originally Posted by Plato
We cannot help until you define what each of $\displaystyle A+B~\&~A-B$ means.

Well, A+B ={$\displaystyle z: z = a+b : a\in{A}; b\in{B}$}.
A-B ={$\displaystyle z: z = a-b : a\in{A}; b\in{B}$}.
• Oct 18th 2011, 06:25 AM
Plato
Re: Describe A + B
Quote:

Originally Posted by Lolyta
Hello. I don't know how to do this(Doh)
A = {$\displaystyle (x_1,x_2): x_1=0, 0 \leq x_2 \leq 1$}
B = {$\displaystyle (x_1,x_2): x_2=2, 0 \leq x_1 \leq 1$}
Describe A+B and A-B.

So it is coordinate operations.
Rewrite the B set to make the answer clearer.
A = {$\displaystyle (x_1,x_2): x_1=0, 0 \leq x_2 \leq 1$}
B = $\displaystyle \{(x_1,x_2):0 \leq x_1 \leq 1, x_2=2\}$

Now
$\displaystyle A+B=\{x_1,x_2): 0\le x_1\le 1, 2 \leq x_2 \leq 1\}$

$\displaystyle A-B=\{x_1,x_2): -1\le x_1\le 0, -2 \leq x_2 \leq -1\}$
• Oct 18th 2011, 06:26 AM
TheChaz
Re: Describe A + B

Quote:

Originally Posted by alexmahone
A + B = {$\displaystyle (x_1,x_2): 0 \leq x_1 \leq 1, 2 \leq x_2 \leq 3$}
A - B = {$\displaystyle (x_1,x_2): -1 \leq x_1 \leq 0, -2 \leq x_2 \leq -1$}

• Oct 18th 2011, 08:38 AM
Lolyta
Re: Describe A + B
Thanks a lot to everyone :)